As House Republican leaders acquiesce to their Tea Party faction and tie a government spending renewal to the defunding of Obamacare, don't look for much cheering from the Senate minority leader's office.

That's because what had largely been House Speaker John Boehner's problem now becomes Kentucky GOP Sen. Mitch McConnell's problem — at least for the next steps of this drama.

The federal government will shut down Oct. 1 unless Congress passes another continuing resolution authorizing further spending. Dozens of Republican lawmakers — led by Sens. Ted Cruz of Texas and Mike Lee of Utah, and helped by the Senate Conservatives Fund, a political committee founded by former South Carolina Sen. Jim DeMint — insist that any such resolution also take away money to implement President Obama's signature health care law.

After initially resisting such a plan, Boehner agreed Wednesday to package the two ideas together and send them to the Democratic-controlled Senate — where it's all but certain to die.

What are the chances that McConnell will be able to pull together the needed votes to prevent Democrats from stripping the Obamacare language out and sending the bill back to the House? Given that a number of Republican senators have already called the linkage strategy a bad idea, probably not so good.

Remember, when Cruz and Lee were circulating their letter promising not to vote for any spending bill that did not "defund" Obamacare, McConnell would not sign it.

All of which means that if and when the Senate eventually passes a "clean CR" back to the House, it could be framed as a failure by McConnell to be an effective enough or conservative enough leader by someone so inclined to see it that way. Someone like, say, Matt Bevin, McConnell's challenger in next year's Republican primary election.